Shares of Amerisource rocketed more than 25 percent in after-hours trade Monday following the news.
Walgreens already holds a 26 percent stake of Amerisource, according to FactSet.
People familiar with the matter told the Journal that the approach was made between representatives of Walgreens Chief Executive Stefano Pessina and Amerisource CEO Steven Collis. The sources told the newspaper, however, that a formal offer hasn't been made and that a deal may not materialize.
Both companies declined to comment to the Journal. The companies also declined CNBC's request for additional comment.
As of its Monday close, AmerisourceBergen had a market value of about $19.6 billion, while Walgreens was about $67.8 billion.